1. Field of the Invention
The present invention is directed to a method for identifying the location in an examination subject of endogenous, in vivo electrophysiological activities occurring in an examination volume.
2. Description of the Prior Art
The measurement, mapping and interpretation of electrical fields generated by electrophysiological activities have long been used in medical diagnostics in the form of electroencephalograms (EEGs) electrocardiograms (EKGs or ECGs). It is also known to measure the magnetic fields generated by such electrophysiological activities using biomagnetic measurement systems. Such systems operate on the principle of, from the measured data, calculating and displaying one or more current dipoles situated inside the examination volume which would generate the magnetic and electrical fields outside the examination volume, which have been measured.
The basic structure and components of such a biomagnetic measurement system are described, for example, in European Application 0 359 864. The extremely weak magnetic fields which are generated by electrophysiological activities are measured by a sensor arrangement, the sensor arrangement generally including a plurality of gradiometers arranged in an array. The position of the electrophysiological activity from which the magnetic fields emanate is identified in the examination volume by interpreting the output signals of the gradiometers. The position of equivalent current dipoles in the examination volume, which generate fields corresponding to the measured fields of the electrophysiological activities, is identified. Proceeding from the values of the magnetic field at a limited number of measuring volume points, therefore, location, strength and direction of the current dipoles must be calculated based on the measured field. This mathematical problem is solved on the basis of models for the biological tissue in the examination volume, and for the equivalent current sources which generate the external field.
In a known method, the solution is achieved using the method of the least squares as described, for example, in "Basic Mathematical and Electromagnetic Concepts of the Biomagnetic Inverse Problem," Sarvas, Physics in Medicine and Biology, Vol. 1932, 1987, pages 11-22. The fundamental parameters of a current dipole are its position in the examination volume and its magnetic moment. In this known method, the positions are entered non-linearly whereas the moments are entered linearly. The minimization of the function of the least squares (least-squares function) can be undertaken with respect to all parameters, or only with respect to the linear parameters. The least-squares function is also referred to as the objective function.
A first minimization method which is extremely intensive in terms of calculating time, is to search for the least-squares in the entire parameter space. This minimization method can supply solutions for a limited number of current dipoles. In practice, however, in order to avoid unreasonably long calculating times, one seeks a solution for a single current dipole. Moreover, the parameter space, which is otherwise six-dimensional, can be reduced by specific models of the examination volume. For cardiological examinations, the examination volume can be replaced by a uniform, conductive, infinite half-space, and for cerebral examinations, the examination volume can be replaced by a uniform, conductive sphere. In a one dipole model, the parameter space is then five-dimensional, and is ten-dimensional in a two dipole model.
A further reduction in the number of parameter can be achieved by introducing locally optimum current dipoles. The minimization of the objective function thereby ensues with respect to the linear parameters of the dipole moment by finding the solutions of a corresponding system of linear equations. Such linearization is discussed in the aforementioned article of Sarvas, and is also discussed in "Multiple Dipole Modeling of Spatic-Temporal MEG Data", Mosher et al., Proceedings of SPIE Conference on Digital Image Synthesis and Inverse Optics, Vol. 1351, July 1990, pp. 364-375. The linear equations connect the dipole moments and the measured values to the points of the measurement space. The solution can be considered in the so-called overdefined case and in the so-called underdefined case. The overdefined solution leads to the concept of locally optimum dipole moments. For each point of the examination volume, the moment of a current dipole situated at that point is defined such that the field generated at the points of the measurement volume by that current dipole best coincides with the field measured at the points of the measurement space.
Locally optimum dipole moments are dependent on the dipole positions. The target function can therefore be considered exclusively as a function of the space. The dimension of the parameter space is thus considerably reduced. This has useful consequences and enables an improvement of the localization algorithm. In a one dipole model, moreover, the entire function can be graphically portrayed in the region of interest.
The objective function F for pointlike sensors or detectors can be calculated on the basis of the following equation: ##EQU1##
In equation (1) bi is the theoretical or actual magnetic field component generated by a current dipole, mi is the measured magnetic field component along the normal of each detector, i.e., the field measured at the points of the measurement volume along the normals prescribed by the orientation of the detector, and M is the number of detectors or points of the measurement space. A objective function having locally optimum current dipole moments in the one dipole model is shown as an example in FIG. 1. As noted above, the minimum of the objective function with respect to the current parameters is sought for identifying the location of the dipole. In known iteration methods such as, for example, the Levenberg-Marquardt Algorithm, there is always the risk that a secondary minimum, such as point B in FIG. 1, rather than a global minimum, which is point A in FIG. 1, will be found.